b: x=8 nên x+1=9
\(F=x^{13}-9x^{12}+9x^{11}-9x^{10}+...-9x^2+9x-2\)
\(=x^{13}-x^{12}\left(x+1\right)+x^{11}\left(x+1\right)-x^{10}\left(x+1\right)+...-x^2\left(x+1\right)+x\left(x+1\right)-2\)
\(=x^{13}-x^{13}-x^{12}+x^{12}+...-x^3-x^2+x^2+x-2\)
=x-2
=8-2
=6
a: \(x^2+55=4y^2\)
=>\(x^2-4y^2=-55\)
=>(x-2y)(x+2y)=-55
=>\(\left(x-2y\right)\left(x+2y\right)=1\cdot\left(-55\right)=\left(-55\right)\cdot1=\left(-1\right)\cdot55=55\cdot\left(-1\right)=5\cdot\left(-11\right)=\left(-11\right)\cdot5=\left(-5\right)\cdot11=11\cdot\left(-5\right)\)
TH1: \(\left\{{}\begin{matrix}x-2y=1\\x+2y=-55\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=-54\\x-2y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-27\left(loại\right)\\x-2y=1\end{matrix}\right.\)
TH2: \(\left\{{}\begin{matrix}x-2y=-55\\x+2y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=-54\\x+2y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-27\left(loại\right)\\x+2y=1\end{matrix}\right.\)
TH3: \(\left\{{}\begin{matrix}x-2y=-1\\x+2y=55\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=54\\x-2y=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=27\\2y=x+1=28\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=27\\y=14\end{matrix}\right.\left(nhận\right)\)
TH4: \(\left\{{}\begin{matrix}x-2y=55\\x+2y=-1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=54\\x-2y=55\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=27\\2y=x-55=27-55=-28\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=27\\y=-14\left(loại\right)\end{matrix}\right.\)
TH5: \(\left\{{}\begin{matrix}x-2y=5\\x+2y=-11\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=-6\\x-2y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\left(loại\right)\\2y=x-5=-3-5=-8\end{matrix}\right.\)
TH6: \(\left\{{}\begin{matrix}x-2y=-11\\x+2y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=-6\\x+2y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\left(loại\right)\\x+2y=5\end{matrix}\right.\)
TH7: \(\left\{{}\begin{matrix}x-2y=-5\\x+2y=11\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=6\\x-2y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\2y=x+5=3+5=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=3\\y=4\end{matrix}\right.\left(nhận\right)\)
TH8: \(\left\{{}\begin{matrix}x-2y=11\\x+2y=-5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=6\\x+2y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\2y=-5-x=-8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=3\\y=-4\left(loại\right)\end{matrix}\right.\)
